3: Transit Network Reliability: An Application of Absorbing Markov Chains

An absorbing Markov chain model is applied to transit assignment to analyse the impact of vertex failure on the probability of trip failure. Vertex failure probabilities are treated as either known or unknown, and if unknown then worst vertex failure probabilities are sought. Lessons learnt from recent random graph research on the robustness of different network topologies are reviewed. An analysis of a number of elemental transit network topologies using the absorbing Markov chain model shows that the hub-and-spoke graph is the most robust to random vertex failure but also among the most vulnerable to directed vertex attack. A particular form of unreliability, namely the probability of being unable to board a transit line due to insufficient capacity, is analysed using the absorbing Markov chain model.